Question
A grid is shown with a rectangle drawn on it. The rectangle is 3 units long and 2 units wide, labeled with 3 and 2 respectively.
Scale: 1 box = 15 feet
Convert this scale drawing so that it has a scale of 1 box = 5 feet. The width in the scale drawing shown is 2 boxes. What will be the width in boxes of the new scale drawing?
Scale: 1 box = 15 feet
Convert this scale drawing so that it has a scale of 1 box = 5 feet. The width in the scale drawing shown is 2 boxes. What will be the width in boxes of the new scale drawing?
Answers
GPT-4o mini
To convert the scale of the drawing, we need to understand the relationship between the original scale and the new scale.
The original rectangle has a width of 2 boxes, and each box represents 15 feet. Therefore, the actual width in feet is:
\[
\text{Width in feet} = 2 \text{ boxes} \times 15 \text{ feet/box} = 30 \text{ feet}.
\]
Now, we want to convert this width to the new scale where 1 box represents 5 feet. To find out how many boxes this 30 feet corresponds to in the new scale, we divide the total width in feet by the new scale value (5 feet per box):
\[
\text{New width in boxes} = \frac{30 \text{ feet}}{5 \text{ feet/box}} = 6 \text{ boxes}.
\]
Thus, the width in boxes of the new scale drawing will be **6 boxes**.
The original rectangle has a width of 2 boxes, and each box represents 15 feet. Therefore, the actual width in feet is:
\[
\text{Width in feet} = 2 \text{ boxes} \times 15 \text{ feet/box} = 30 \text{ feet}.
\]
Now, we want to convert this width to the new scale where 1 box represents 5 feet. To find out how many boxes this 30 feet corresponds to in the new scale, we divide the total width in feet by the new scale value (5 feet per box):
\[
\text{New width in boxes} = \frac{30 \text{ feet}}{5 \text{ feet/box}} = 6 \text{ boxes}.
\]
Thus, the width in boxes of the new scale drawing will be **6 boxes**.